For BNCT of melanoma metastases in the brain, it has been necessary to calculate the dose distributions in the patient for dozens of possible neutron beams and then to combine manually the different beams by individually weighting and adding them. This time consuming approach eventually gave the required treatment plan, which satisfied the prescription dose. However, by linear optimisation with the Simplex method, the optimum weights for a set of beams can be determined mathematically. The objective function to maximise is the minimum averaged physical boron dose in one certain lesion for every set of beams. The maximisation of this objective function is performed under the constraints of certain maximum and minimum dose limits in the organs at risk and lesions respectively and restricting the set of weighted beams to deliver an
average total weighted dose of 7 Gy in the brain. After iteration, by using the constraint set for the minimum dose in the lesions as a variable and performed for all combinations of the neutron beams, the optimum beams and weights are found for each treatment. As a preliminary result, the total irradiation time decreased by more
than 30%, which is advantageous regarding both the pharmacokinetics of the boron in the patient and patient comfort.